It is known in the art of injection molding to simultaneously or sequentially inject two melt streams of moldable material into a mold cavity using a single hot runner injection molding nozzle, which is commonly referred to as coinjection. A conventional manner of controlling the flow of two or more melt streams through the nozzle and into a mold gate and subsequently the cavity has been provided by rotating a valve pin member of the nozzle to align different melt channels or by axially reciprocating a valve pin member and one or more valve sleeve members, which surround the valve pin member, of the nozzle between open and closed positions. Although many systems have been developed utilizing a valve pin member and a valve sleeve member that are axially reciprocated to provide simultaneous or sequential injection of two or more melt streams, such arrangements are not without their deficiencies, such as inaccuracies in reciprocating movement and difficulties in keeping the melt streams adequately separated, as well as adding complexity to the manufacture, assembly, and operation of the hot half of the injection molding systems. Another deficiency in such systems is that it is difficult to align a valve sleeve member and/or a valve pin member with the mold gate, such aligning being important for improving injection technique and reducing gate wear.